Modern aircraft, in particular transport planes, have fuel pipes which allow fuel to be transported between different portions of said aircraft. In particular, as shown in FIG. 1, a plane 1 has a first fuel pipe 4 between a central tank 2, 2a, 2b situated in a central portion of the plane (central section and/or wings) and an auxiliary power unit (APU) 8 situated in the rear portion of the plane's fuselage, so as to supply fuel to said APU device. Some planes also have an auxiliary tank 6 situated in the rear portion of the plane's fuselage or in a stabilizer fixed on this rear portion of the fuselage. In a case of this kind, a second fuel pipe 5 is disposed between this auxiliary tank 6 and the central tank 2, so as to allow exchanges of fuel between these tanks. These fuel pipes are of double-skinned design, so as to prevent fuel from being able to spread in the plane in the event of a leak. A fuel pipe of this kind is therefore made up of an internal pipe inserted in an external pipe. For practical installation reasons in the plane, this fuel pipe is made up of a plurality of sections assembled together and fixed to the plane's structure by means of supports. A first and a second consecutive section are thereby assembled together thanks to an assembly device. As depicted in FIG. 2, this assembly device 14 has a clamp 28 allowing one end of the internal pipe 20a of the first section to be assembled with one end of the internal pipe 20b of the second section. This assembly device likewise comprises a coupling device 24 allowing one end of the external pipe 22a of the first section to be assembled with one end of the external pipe 22b of the second section. For practical installation reasons in the plane, this end of the external pipe 22b of the second section comprises a part 26 which can, moreover, guarantee a fixing function to the structure of the plane. Sealing gaskets 30 are provided to guarantee the tightness of the assembly device 14. However, when the plane is in flight, its structure is subjected to deformations which can sometimes lead to leaks affecting the assembly devices 14 between the different sections of a fuel pipe fixed to said structure. In a case of this kind, fuel may be discharged at the clamp 28 between the first internal pipe 20a and the second internal pipe 20b. Given that the fuel pipe is double-skinned, the fuel which is discharged at the clamp is retained in the space formed between the internal pipes and the external pipes. As depicted in FIG. 3, a drain 10 is connected to a portion of the fuel pipe 4 representing a low point of said fuel pipe when the aircraft is on the ground. This drain allows any fuel retained in the space formed between the internal pipes and the external pipes to be removed towards the ground. This drain generally also has an indicator 12 which enables a fuel leak in the space formed between the internal pipes and the external pipes to be signaled. This indicator may, for example, be formed by a transparent capsule which fills up with fuel when fuel is discharged through the drain. This allows a maintenance operative to detect a leak of this kind easily. In such a case, the maintenance operative generally checks the assembly devices between the different sections of the pipe. If necessary, he tightens clamps or replaces worn gaskets. Once the maintenance operations are complete, he empties the indicator so that it is once again able to perform its function. However, given the conformation of the coupling device 24 between the external pipes 22a and 22b of the first section and of the second section at each assembly device 14, fuel may remain trapped in the different assembly devices without being discharged through the drain. This phenomenon is illustrated in FIG. 4, which represents an assembly device 14 between two sections of pipes depicted in a substantially horizontal position. The coupling device 24 forms a low point between the external pipe 22a of the first section and the external pipe 22b of the second section in which fuel 32 may accumulate without being able to escape unless the slope of the assembly device and of the pipe sections is modified. A modification of this kind of the slope of the assembly device and of the pipe sections may particularly take place while an aircraft is in flight. This means that following an aircraft maintenance operation in which a fuel leak problem in the space formed between the internal pipes and the external pipes has been solved, a change in the incline of the aircraft during flight can cause fuel which has accumulated in said low point formed by the coupling device to able to escape from said low point and move into the space formed between the internal pipes and the external pipes. This fuel may therefore migrate as far as the drain 10 and fill the indicator 12. Following this aircraft flight, the indicator may therefore contain fuel when there has not been a fresh leak. This may lead a maintenance operative to conduct a fruitless search for a fresh leak, even though the fuel contained in the indicator comes from a previous leak that has already been repaired.